On a server with Plesk installed I have added a CNAME rule pointing from one of the sites subdomains to an external website.

I have checked the named configuration for that domain name and it shows the CNAME however the sub domain just points to the default server page and ignores the CNAME rule. Named has been restarted and I've also run the rvmng reconfigure-vhost command.

EDIT: I just noticed that the site's nameservers aren't on this server but the default doteasy ones so I assume that may be why the rule is ignored. I will change the nameservers and see if that solves it. I'll update here with the outcome. Thanks guys for your tips so far.

EDIT 2: The server only has one IP address so it won't be possible to use custom name servers. Could this be the cause though? When I run dig cname login.example.com it returns:

Why do not you use A records? It is the same zone file, in this case it is much easier (and you can avoid future troubles).

The zone file looks ok btw. You should look with standard tools (like host, dig) to check that it is indeed serving what you see in the file. It also can be that a resolver dns server cached a negative response earier (if you just put these records there).

Tell us the real dns name if you really want a fix!

EDIT:
Sorry I entirely overlooked that you have
socialize.gigya.com
in your records.

On the other hand you are looking at the wrong direction. But I do not bother until you tell your real domain name.

If you are receiving the right records from your Plesk server (see dig command below), then it's a cache issue (old records have been cached by your PC/ISP's nameservers):

# ask A records from Plesk server
# you should see CNAME record in the ANSWER section
dig @plesk.server login.example.com
# or just directly ask for CNAME record
dig @plesk.server login.example.com cname